document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=61942>Question 61942</A>: <I><SPAN STYLE=\"word-break: break-all;\"> i really need help with this but no one has responded...is there anyone who can help? PLEASE!\r<BR>\n" );
document.write( "\n" );
document.write( "fireworks are launched into the air.  the quadratic function that models the fireworks height, s(x), in feet, x seconds after they are launched is given by the equation s(x)=-16x^2+200x+4.  when should the fireworks explode so that they go off at the greatest height? What is that height? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #42655 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=42655\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> fireworks are launched into the air. the quadratic function that models the fireworks height, s(x), in feet, x seconds after they are launched is given by the equation s(x)=-16x^2+200x+4. when should the fireworks explode so that they go off at the greatest height? What is that height?<BR>\n" );
document.write( ":<BR>\n" );
document.write( "This is an ordinary quadratic equation so finding the vertex will give you the value of x when the maximum height is obtained.<BR>\n" );
document.write( ":<BR>\n" );
document.write( "The vertex formula: x = -b/(2*a)<BR>\n" );
document.write( ":<BR>\n" );
document.write( "In your equation a = -16; b = +200<BR>\n" );
document.write( ":<BR>\n" );
document.write( "x = -200/(2*-16)<BR>\n" );
document.write( "x = -200/-32<BR>\n" );
document.write( "x = +6.25 seconds after launch the firework should explode<BR>\n" );
document.write( ":<BR>\n" );
document.write( "To find the actual height of the maximum, substitute 6.25 for x in the original equation:<BR>\n" );
document.write( "s(x) = -16(6.25^2) + 200(6.25) + 4<BR>\n" );
document.write( "s(x) = -16(39.0625) + 1250<BR>\n" );
document.write( "s(x) = -625 + 1250<BR>\n" );
document.write( "s(x) = +625 ft is the max height and occurs after 6.25 sec<BR>\n" );
document.write( ":<BR>\n" );
document.write( "A graphical presentation would help you understand it<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+200%2C+-4%2C+16%2C+-100%2C+700%2C+-16x%5E2+%2B+200x+%2B+4%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+200%2C+-4%2C+16%2C+-100%2C+700%2C+-16x%5E2+%2B+200x+%2B+4%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );